BonaNI-Kouteckj. Buenker, Peyerimhoff
/
The Sudden Polarization Effect
(3) E. Huckel, 2.Phys., 70, 204 (1931). (4) W. Haberditzl, Angew. Chem., lnt. Ed. Engl., 5, 288 (1966); H. J. Dauben, Jr., J. D. Wilson, and J. L. Laity, "Nonbenzenoid Aromatics", Vol. 11, J. P. Snyder, Ed., Academic Press, New York, 1971, Chapter 3. (5) J, Aihara, J. Am. Chem. SOC.,101, 558 (1979). (6) B. Pullman and A. Pullman, "Les Theories Electroniques de la Chimie Organique", Masson et Cie, Paris, 1952, Chapter IX. (7) L. Salem, "The Molecular Orbital Theory of Conjugated Systems", W. A. Benjamin, New York, 1966, Chapter 4. (8) M. Mayot, G.Berthier, and B. Pullman, J. Phys. Radium, 12, 652 (1951); G. Berthier, M. Mayot, and 8 . Pullman, ibid., 12, 717 (1951); G. Berthier, M. Mayot, A. Pullman, and B. Pullman, ibid.. 13, 15 (1952); M. Mayot. G. Berthier, and B. Pullman, J. Chim. Phys. Phys.-Chim. Bid., 50, 176 (1953). (9) R. McWeeny, Mol. Phys., 1, 311 (1958). (10) J. Gayoso and A. Boucekkine, C. R. Acad. Sci.. Ser. C, 272, 184 (1971). (11) R. 8. Mallion, Proc. R. Soc. London, Ser. A, 341, 429 (1975), and many references cited therein. (12) See, e.g., R. J. Wilson, "Introduction to Graph Theory", Oliver and Boyd, Edinburgh, 1972. (13) J. Aihara, J. Am. Chem. SOC.,96, 6840 (1976). For the application of a generalized Sachs theorem to heterocyclic conjugated systems, see ref 17. (14) A. Graovac. 0. E. Polansky, N. Trinajstic, and N. Tyutyulkov, 2.Naturforsch. A, 30, 1696 (1975).
5917
(15) H. Sachs. Publ. &th,(Debrecen),
11, 119 (1964); A. Graovac, I. Gutman, N. Trinajstic, and T. Zivkovic, Theor. Chim. Acta, 26, 67 (1972). (16) H. Hosoya. Theor. Chim. Acta, 25, 215 (1972). (17) J. Aihara, J. Am. Chem. Soc., 96, 2750(1976). (18) H. Hosoya, Bull. Chem. Soc.Jpn., 44, 2332 (1971). (19) R. McWeeny. Roc.phys. Soc., London, Sect. A, 64,261 (1951); J. A. Pople, Mol. Phys.. 1, 175 (1958). (20) G. Hazato, J. Chem. Phys., 27, 605 (1957). (21) I. Gutman, M. Miiun, and N. Trinajstic. J. Am. Chem. SOC., 99, 1692 (1977). (22) The realness of the roots of the same polynomial as the reference polynomial (eq 4) has already been proved by 0. J. Heilmann and E. H. Lieb, Commun. Math. Phys., 25, 190 (1972). This proof warrants the realness of the resonance energy defined in ref 17 and 21. Professor L. J. Schaad kindly brought my attention to the Heiimann-Lieb paper. (23) M. J. S.Dewar and G. J. Gleicher, J. Am. Chem. Soc., 87,685,692 (1965); M. J. S. Dewar and C. de Llano, ibid.. 91, 789 (1969). (24) J. Aihara, J. Am. Chem. SOC., 99, 2048 (1977). (25) C. A. Coulson, J. A. N. F. Gomes, and R. B. Mallion, Mol. Phys., 30, 713 (1975). (26) J. Aihara, Bul/. Chem. SOC.Jpn., 50, 2010 (1977); 51, 1788 (1978). (27) H. P. Figeys, Chem. Commun., 495 (1967). (28) See.e.g.. R. C. Haddon, V. R. Haddon. and L. M. Jackrnan, Top. Cum. Chem., 16, 103 (1971). (29) J.-F. Labarre and F. Crasnier, Top. Curr. Chem., 24,33 (1971); R. Breslow, Acc. Chem. Res., 8, 393 (1973).
Use of Configuration Selection Methods to Study the Sudden Polarization Effect Vlasta BonatiL-Kouteckj,*la Robert J. Buenker,lb and Sigrid D. PeyerimhofflC Contributionfrom the Institut fur Physikalische Chemie und Quantenchemie, Freie Universitat Berlin, 1000 Berlin 33, West Germany, the Lehrstuhl fur Theoretische Chemie, Gesamthochschule Wuppertal, 5600 Wuppertal 1 . West Germany, and the Lehrstuhl fur Theoretische Chemie, Universitat Bonn, 5300 Bonn, West Germany. Receiljed April 4 , 1979
Abstract: The variation of the dipole moment of twisted ethylene as a function of the angle of pyramidalization of one CH2 group is determined for a variety of A 0 basis sets and levels of CI treatment. The results for moderate amounts of pyramidalization are seen to be strongly dependent on the choice of one-electron basis functions in the CI, although for still larger angles (20' and beyond) this effect becomes much less important. Configuration selection methods prove to be very effective in this investigation, making feasible the extension of such calculations to more chemically interesting systems than would otherwise be possible.
I. Introduction The high polarizability of the lowest singlet excited states in hetero- and nonsymmetrical biradical systems is easily understandable from a physical point of vie^^-^ and the possible experimental consequences of this phenomenon have received wide attention in recent y e a r ~ . ~ In - I discussing ~ this effect it is obviously important to have quantitative information about the manner in which the electronic charge is redistributed as either the internuclear geometry of such biradicals is varied or the nature of their substituents is changed. It is therefore desirable that theoretical methods be developed which are capable of giving a reliable description of large charge displacements which occur as a result of a relatively small perturbation a t one of the radical centers. One of the simplest examples in which this "sudden polarization" effect can be studied is in the first two singlet excited states of twisted ethylene as one of its CH2 groups is pyrami d a l i ~ e d . ~ The ~ . ~ geometrical ,'~ change in question is accompanied by a reduction in the molecular symmetry from D2d to C,, and thus to describe the polarization effect properly it is necessary to achieve a smooth transition from the delocalized to the localized representation of a biradical (compare ref 16, 1 1, and 15). A proper description of the pyramidalization of 5 9 1 5
0002-7863/79/150l-5917$01 .OO/O
ethylene places severe demands on the theoretical method employed since it requires an accurate determination of the balance between two highly polarizable centers which are a t the same time only weakly interacting. In the framework of a general configuration interaction treatment these considerations imply that great care must be taken in the choice of the configuration space used in the calculations, including the one-electron basis from which the requisite determinantal functions are formed. On the other hand, if relatively flexible A 0 basis sets are to be used and more chemically interesting systems than ethylene are to be studied in future applications, it is clear that the extent of the CI must be kept as limited as possible, consistent with the above accuracy requirements. The present paper thus presents a series of truncated CI calculations using a variety of A 0 and MO (or NO) basis sets in order to describe the sudden polarization effect in the lowest two singlet excited states of ethylene, with the ultimate goal of being able to design practical theoretical treatments which are applicable to larger organic biradical systems. 11. Nonpyramidalized Twisted Ethylene Treated in C,
Symmetry Because of the D2d symmetry of 90' twisted ethylene none of the electronic states in this conformation can possess a 0 1979 American Chemical Society
Journal of the American Chemical Society
5918
/
101:20
/ September 26, 1979
Table I . 90’ Twisted Ethylene in C, Symmetry (Zero Pyramidalization)
trcatrnentO A, ‘A”
2M (6238)
extrapolated energies ( T = O ) b T, for S I and S z yhartrees
-17.9555 -11.9495
0 3 5 1
B, ’A”
-77.9624
ZM (1189)
-71.9570
3 5 15
B, ’A”
-17.9731
1 3
4 M (21 093)
B, NO(Sl) 4M (21 093)
-11.9686 -11.9144 -77.9699
C, ‘A”
-78.0675
2 M (19431) C, ’A’’
-1 8.063 5
5
4M (53 611)
15
5 25 5 10 20 30
-78.0840
10
-18.0805
20 30
sec eq order
E , au
6238 2603 2393 2950 2412 2230 1622
-11.9555 -71.9531 -11.9521 -11.9622 -11.9612 -71.9604 -11.9556
5891 4200 3371 1981
-17.9729 -11.9708 -11.9688 -11.9601
2402 1410 5064 3927 2812 2242 4104 2970 2198
-71.9136 -11.9638
first root S I CI/CZ y)f 0.991 0.98 1 .oo 0.991 1.003 1.033 1.089 1.023
y(z)
0.00
0.00
0.006
0.0 1
0.00
-0.05
0.00
-0.01
1.056 1.029
0.00
-0.09
0.00
-0.21
-78.0625 -18.0561 -18.0451 -18.0342
1.069 1.183 1.170 1.262 1.189 0.772
0.00 0.00
-0.63 -0.94
-18.0612 -78.0456 -18.0328
0.926 1.012 0.11 1
0.00
1.010
0.23
E , au
second root S2‘ CliC2 P(Y)
-11.9495 -77.9472
- 1.002
-77.9462 -11.9568 -71.9551 -11.9547 -11.9502 -11.9611 -17.9656 -17.9636 - 77.95 5 2 -11.9690 -77.9640
-1.00 - 1.003 -0.997 -0.970 -0.9 19 -0.98 1 -0.989 -0.946 -0.914 -0.935 -0.848
-78.0587 -78.0524 -78.0418 -18.0308 -78.0576 -78.0420 -18.0288
dz)
0.00
-0.003
0.00
-0.02
- 1.04
0.00
0.13
0.00
0.06
0.00
0.19
0.00
0.21
-0.857 -0.194 -0.842 - 1.131
0.00
0.63 0.94
- 1.080 -0.93 1 - 1.294
0.00
0.00
-0.25
+
Given are the A 0 basis (A: C(9s5p/4s2p), H(4s/2s) (ref 19 and 5), B: C(9s5p/5s2p), H(5s/2s) (ref 19); C: B Id orbital a t C atom with N = O h ) , the one-electron basis for CI (3A” S C F MOs, NOS for S I , o r . . .la‘2 S C F MOs), the number of reference configurations n M (see acction I I, selection based on two ‘A’ roots, S I and S2), and the corresponding size a t the CI space for all single and double excitations ( T = 0). For details concerning the extrapolation technique, see ref 19. Given are energies and dipole moments (D) for the lowest two excited slatcs (SIand S2) and the CI coefficient ratio C I / C ~for the leading configurations (1) and (2) for each IA’ state (definition of configurations i \ given i n section 11). Energies obtained for T = 0 without extrapolation.
permanent dipole moment. Provided that an equivalent A 0 basis is assumed for each biradical center it is clear that this feature will be mirrored in any full CI treatment, but once the configuration space is truncated in any way the value of the dipole moment becomes dependent on the choice of the oneelectron basis used to construct the individual determinantal functions. As long as the MO basis functions transform according to the irreducible representations of the full D 2 d point group (or the D2 subgroup) it is easy to find sets of configurations which lead to the correct (vanishing) dipole moment result for the states of twisted ethylene. If the MOs are merely C‘, (or C2,) symmetry orbitals, however, it becomes quite difficult to find a smaller than full CI space which produces a zero dipole moment; since the highest molecular symmetry for pyramidalized conformations is C, this situation must be taken into account in trying to arrange for a smooth transition from symmetrical to nonsymmetrical ethylene geometries. Furthermore, even if the M O basis does possess a t least 0 2 symmetry, it is nevertheless true that corresponding CI spaces can still be found which do not produce the proper balance between the two radical centers in a D2d nuclear conformation. I n designing C I treatments which are to faithfully represent the change from pyramidalized to nonpyramidalized geometries it is important to keep both of the above problems of C I truncation and symmetry imbalance in M O basis in mind. On the one hand it is obvious that any calculation is unsatisfactory which does not yield a zero dipole moment for nonpyramidalized geometries, but on the other it must be accepted that there is no guarantee that a treatment which is constrained to give the correct result in this case will be of suitable accuracy when the degree of pyramidalization is large. In order to investigate these points in a systematic manner a series of truncated CI calculations has been carried out for the nonpyramidalized ethylene conformation and the results are collected in Table I. The treatments considered are of the multireference dou-
ble-excitation CI (MRD-CI) type with configuration select i ~ n . ’ ~Two . ’ ~different sets of reference configurations are thereby considered. In the 2M2R calculations the reference configurations are
. . . 3a’2 4a’2 5af26a’2 l a N 27ar2
(2)
in C,, notation (a core of the two-carbon inner-shell orbitals is maintained .throughout) while in the more extensive 4M2R treatment these are supplemented by two other species:
. 3a’2 4ar25a’2 6a‘2 l a ” 7ar22a” . . . 3a’2 4ar25a’ 6a’2 la”2 7a’ 2aN2
(3) (4)
which are found to be the most important secondary configurations in the expansions of the two excited singlet states. I n a given A 0 and M O basis all single and double excitations are generated with respect to n-reference configurations (nM) and selection is made based on the results of the lowest two IA’ roots (2R) in small secular equations, including test and reference configurations (compare ref 18). Only configurations resulting in an energy lowering greater than a given threshold value T a r e included in the final secular problem; for T = 0 all configurations obtained by single and double excitations with respect to the reference configurations are included. Three different A 0 basis sets and three different one-electron basis sets for the CI have been used in this work. The smaller A 0 bases are basically of contracted Gaussian double {character. I n Dunning-Huzinaga notationlg bases A and B are C(9s5p/4s2p), H(4s2s) (compare also ref 5) and C(9s5p/5s2p), H(5s/2s), respectively. The A 0 basis C is an extension of the bases B, adding one d orbital a t each carbon with exponent 0.6. The one-electron basis obtained from the triplet SCF calculations 3A” (3A2)has been used for building up the CI space of the two singlet excited states ]A’ (SIand S2). The natural
BonaMt-Kouteckj, Buenker, Peyerimhoff
/
The Sudden Polarization Effect
5919
Table 11.90’ Twisted Ethylene with 5’ Pyramidalization of One CH2 Group
trcatrnentO
extrapolated energies ( T = O ) b T, for S I and S2 phartrees
sec eq order
E , au
first root SlC
0 3 5
6238 2964 2628
1 5 10 15
second root S2‘
C I / C ~ p(y)
p(z)
E , au
CI/C2
P(v)
Y(Z)
-77.9552 -71.9532 -71.9520
0.900 0.898 0.892
0.13
0.39
-77.9492 -11.9412 -17.9460
-1.110 -1.114 -1.119
0.12
-0.38
3818 2168 2302 2033
-11.9618 -11.9591 -11.9574 -11.9554
0.865 0.921 I .022 0.996
0.14 0.13
0.57 0.33
-11.9564 -77.9543 -11.9520 -17.9 500
-1.158 -1.085 -0.979 - 1.003
0.11
-0.59
591 1 4020 2866 2299
-77.911 1 -71.9678 -11.9632 -11.9588
0.953 0.955 0.970 1.080
0.15 0.15
0.16 0.16
-11.9658 -71.9625 -77.9579 -11.9535
-1.041 -1.047 - 1.032 -0.924
0.14 0.14
-0.15 -0.15
A , ’A”
-77.95 5 2
2 M (6238’)
-71.9492d
B, 3A”
-11.9623
2 M (1189)
-11.9568
B, 3 A n
-71.9132
4 M (21 093)
- 77.9680
2 5 10 15
B. NO(Si)
-17.9739 -11.9694
5 25
3486 1811
-11.9126 -71.9654
0.138 0.142
0.16
0.99
-11.9619 -77.9608
-1.35 - 1.34
0.11
-0.96
4 M (21 093) C , ’A”
-18.0675
-78.0549 -1 8.0441 -18.0352
0.989 1.200 0.114
0.05
-18.0513 -18.0413 -78.0316
-1.01 1 -0.833 - 1.395
0.1 1
-0.04
-18.0635
4608 3380 2648
0.11
ZM(19431)
10 20 30
C , ’A“
-18.0830
-78.0583 -18.0430 -78.0306
0.947 1.198 0.968
0.19
-78.0549 -18.0395 -18.0211
-1.051 -0.837 - 1.033
0.12
-0.21
-78.0195
5212 3266 2429
0.12
4 M ( 5 3 617)
10 20 30
See footnotes to Table I orbitals of the S I state have been utilized as the second type of one-electron basis set for the CI(NO(S1)). Finally the S C F MO’s of the . . .3a’2 4a’2 5a‘2 6a’* laN27a’2 configuration were employed as well. None of the one-electron basis sets employed has been constrained to have the full D2d symmetry, so as indicated above there is no requirement that a t T = 0 the calculated dipole moments should vanish, but nevertheless both the 3A” (3A2)M O and ‘A’ ( S I ,‘ A I ) N O sets are sufficiently symmetrical that this condition holds to a good approximation. The dipole moment results are found to be relatively sensitive to the choice of the selection threshold down to a value in the 1.0-5.0-phartree range. The variation of the mixing coefficients C I / C ~of the leading two terms ( I ) and (2) is quite instructive in this regard, since this information has been obtained for more T values than have the dipole moments themselves (cf. Table I). In general the absolute value of this coefficient ratio serves as a measure of both the magnitude and direction of the polarization in a given electronic state ( I C I / C ~ ~ < I corresponds to positivep(z) values; I c ~ / c ~ I > 1, to negative p ( z ) values). In the smaller two A 0 basis sets it is seen that for sufficiently small T values the magnitude of the dipole moment (or Icl/c2l) is essentially independent of the selection threshold (within a few hundredths of a debye). For the larger A 0 basis C (with a single carbon d function) this condition is more difficult to attain because of the generally larger secular equations which arise in this case. Nevertheless it is clear from the general appearance of Table I that the desired numerical stability can be achieved for CI secular equations which are substantially smaller in order than their T = 0 counterparts. A second point of interest concerns the energy values obtained in the various CI treatments. For high T values and small numbers of reference configurations rather large distinctions in energy are noted for the various one-electron basis sets, but, when the eigenvalue results for the larger reference sets are extrapolated to zero threshold, such differences disappear to a large extent (Table I). In other words, from an energy point of view it is difficult to make an unambiguous judgment as to the quality of the MOs or NOS for such levels of theoretical treatment. Finally it should be noted that the highly asymmetrical S C F MOs of the . . .3a’* 4a’2 5a’2 6a’2 1 a” 7a’2 configuration lead to an incorrect (nonzero) dipole
moment which is virtually independent of selection threshold variation (at least up to T = 25 phartrees). 111. Pyramidalized Conformations
If the geometrical perturbation a t one of the carbon atoms is small, as, for example, in the case of 5’ pyramidalization for one CH2 group, the two singlet excited states are still close enough together in energy to cause their dipole moments to be sensitive to the value of the selection threshold in the CI treatment (Table [I). When numerical stability is obtained several interesting results emerge, however. First, comparison of CI treatments with two and four reference configurations indicates that the calculated magnitude of the polarization is smaller in the latter case. Secondly, the results are found to be even more dependent on choice of MO basis, with natural orbitals obtained for the lowest excited ‘A’ states producing significantly larger dipole moment values (-1 D) than are found in an analogous (4M2R) CI treatment based on 3A” MOs (0.22 D). The amount of polarization i n the N O case is very similar to that found by Brooks and Schaefer5 using orbitals optimized for an equal mixture of the two leading configurations. (These orbitals were employed in a 2M2R CI a t zero selection threshold for A 0 basis A). Finally it is noted that at this pyramidalization angle the dipole moment results in the largest A 0 basis C (with d functions) are less sensitive to the choice of selection threshold than a t 0”. Increasing the amount of geometrical perturbation in twisted ethylene still further leads to a substantial reduction i n the dependence of the dipole moment results on the magnitude of the threshold T , as can be seen from Tables I11 and IV. Nevertheless, in some respects the results for 10’ pyramidalization show a quite similar behavior as those for 5’. In particular expanding the reference set from two to four configurations is found to lead to a slight reduction in the amount of calculated polarization, and the choice of A 0 basis is seen to play a rather minor role in such results. Furthermore, the CI treatment using NOS obtained for the lowest ‘A’ root ( S I ) again yields much larger diple moment values than those which result when triplet S C F MOs are employed; for example, in the 4M2R calculations a distinction of 1.6 D is noted at this angle. The extrapolated T = 0 energy eigenvalues for the two sets of one-electron functions are seen to differ by at most 0.003
5920
Journal of the American Chemical Society
/
101:20
/ September 26, 1979
Table 111. 90' Twisted Ethylene with 10' Pyramidalization of One CHI Group
treatmenta
extrapolated energies ( T = O ) b T, for S I and S2 phartrees
first root SI
sec eq order
E , au
0 3 5 IO 50
6238 3148 3210 2651 1262
-11.9541 -11.9524 -71.9512 -11.9489 -71.9343
0.664 0.668 0.652 0.655 0.121
0.33
1.44
0.32 0.31
1.53 1.52
4495 3666 3178 2632
-71.9615 -17.9604 -71.9594 -11.9515
0.621 0.641 0.666 0.665
0.34
1.17
0.31
1.56
5184 4645 3381
-11.9696 -11.9611 -17.9631
0.682 0.612 0.618
0.35 0.35
0.268 0.285
A,3A"
-77.954Id
2 M (6238)
-11.9483
B,'A"
-11.96 I 9
1 3
2 M (7789)
-71.9556
5 IO
B.'A"
-71.9725
3 5
4 M (21 093)
-71.9611
IO
second root S 2 c
E,au
CIIC2
rCv)
P(Z)
-11.9483 -71.9461 -11.9448 -77.9429 -77.9288
-1.500 -1.491 -1.521 -1.519 -1.314
0.17
-1.42
0.16 0.15
- 1.52 - 1.52
-11.9556 -11.9546 -11.9536 -11.95 I 6
-1.592 -1.532 - 1.495 - 1.495
0.17
-1.12
0.17
- 1.55
1.20 1.26
-77.9641 -71.9621 -11.9583
-1.451 -1.481 1.461
0.21 0.21
-1.17 -1.24
0.45
2.86
-11.9654 -17.9624
-3.613 -3.399
0.10
-2.83
c 1 / ~ 2 poi)
-
B.NO(S 11 4 M ( 2 1 093)
-11.9153 -71.9612
5 15
3245 2231
-11.9139 -11.9705
B,. . .7a'*MO 4 M (21 093)
-71.9710 -17.9596
2 6
5601 4032
-11.9163 -11.9147
0.1 11 0.103
0.46
3.31
-77.9581 -17.9552
-2.942 -3.001
0.06
-3.15
C.3A"
-7 8.0665
-18.0560 -18.0457 -18.0374
0.641 0.516 0.103
1.70
-78.0521 -78.0420 -18.0337
-1.539 - 1.128 -1.418
0.13
- 1.69
-78.0630
5133 4036 3240
0.27
4 M ( I 9 431)
IO 20 30
C,'A"
-78.0825
20 30 40
3958 2912 2331
-78.0438 -78.0337 -18.0225
0.655 0.549 0.706
0.30
1.48
-18.0404
-1.525 -1.810 -1.41 1
0.16
- 1S O
4 M ( 5 3 617)
-18.0790
~~
-18.0291 -78.0188
See footnotes to Table I. Table IV. 90" Twisted Ethylene with 20' Pyramidalization of One CH2 Group
treatmenta
extrapolated energies ( T = O ) b T, sec eq for S I and Sz phartrees order
/\,'A"
-77.9542d
2 M (6238)
-77.9433d
B,'A"
-71.9601
first root Sic
second root
CIICZ 1101) dz)
E , au
S2c
E.au
CI/C2
POI)
A Z )
0 3 5
6238 4431 3918
-17.9542 -11.9521 -11.9509
0.272 0.211 0.260
0.81
3.27
-11.9433 -17.9413 -11.9398
-3.602 -3.606 -3.162
0.13 -3.1
5
-11.9590 -11.9561 -11.9547
0.261 0.269 0.283
0.82
3.62
-77.9481 -17.9461 -17.9448
-3.110 -3.653 -3.412
0.13 -3.4
0.262 0.269 0.25 1
0.81
2.98
-77.9519 -77.9538 -77.9502
-3.741 -3.664 -3.923
0.21 -2.8
0.88
3.36
-77.9538 -71.9494
= 0.929 = 0.932
0.11 -3.1
= 0.871 = 0.872
0.15 -3.2
2 M (7789)
-77.9502
15
3686 3963 2609
B.'A"
-77.9127
5641 3963 3213
-11.9611 -71.9633 -11.9600
IO
4 M (21 093)
-77.9622
5 10 15
B, NO(S1) 4 M (21 093)
-77.9779 -77.9560
5 15
3833 2481
-71.9764 -17.9122
~2
= 0.955
~2
= 0.957
B.. . .7a'*MO 4 M ( 2 1 093)
-17.9771 -71.9543
3 5
5541 4659
-11.9166 -77.9151
~2 = c2=
C.'A"
-78.0610
-18.0465 -18.0367 -18.0297
0.165 0. I75 0.171
4.00
-18.0368 -78.0278 -78.0209
-5.94 -5.61 -5.68
0.08 -3.9
-78.0555
4846 3164 3156
0.72
2v
20 30 40 20 30 40
4930 3683 2851
-18.0465 -18.0349 -78.0245
0.150 0.166 0.145
0.71
3.59
-78.0366 -78.0265 -18.0155
-6.53 -5.93 -6.12
0.13-3.5
(19431)
C.'A"
-18.0860
4 M ( 5 3 617)
-78.0720
0.956 0.957
0.88
3.49
-77.9515 -77.9491
CI
CI
CI C]
(' See footnotes to Table I. hartree for both ' A ' roots, with the NOS being slightly preferred. I n this connection it is also worth noting that the SCF MOs for t h e . . .3a'2 4a'2 5a'2 6a'2 laN27a'2 configuration lead to the lowest 4M2R CI extrapolated T = 0 energy and a dipole moment result which is only 0.5 D larger than what is obtained with first-root NOS. It thus would appear that, although the problem with the dependence of the dipole moment results on selection threshold is greatly alleviated for 10' pyramidalization, the CI treatment is still not able to fully overcome the unbalanced description of the biradical centers inherent in a given one-electron basis set.
Finally, as the angle of pyramidalization is increased to 20' and beyond, the dependence of the calculated polarization on selection threshold has all but disappeared and the choice of MO basis is found to be a far less critical factor than in the 5- IOo range. In the respective 4M2R treatments for the B A 0 basis at 8 = 20° the dipole moment for the lowest 'A' state (SI) varies from only 3. I O to 3.47 D for use of the 3A" MOs and 'A' NOS, respectively, while the analogous results for 30' pyramidalization are even more similar to one another (3.83 vs. 3.79 D). By contrast the nature of the A 0 basis appears to become a n increasingly important factor for larger geometrical per-
BonaMC-Kouteckc. Buenker. Peyerimhoff
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The Sudden Polarization Effect
turbations, with the addition of carbon d functions leading to an increase of 0.5 D in the dipole moment of the lowest 'A' state compared to the results obtained when the smaller basis sets A or B are employed; calculations carried out at still smaller selection threshold ( T = 20 phartrees) for the C basis would be desirable before being certain on the actual magnitude of this effect, however (Table IV). As for the corresponding energy results, it is noted first and foremost that the pyramidalization surface for S I is very flat. Nevertheless, there is a definite tendency for the energy to decrease toward approximately -3 kcal a t 0 = 30', even though for small angles the calculations do indicate a slight barrier (
